Adjustable correcting networks



0 J. OSWALD 2,948,866

' v ADJUSTABLE CORRECTING NETWORKS Filed Nov. 5, 1958 2 Sheets-Sheet 1 q R3 Rb WVBMTOR Jacques qswALa 5v W Q 2 A TTOkA/EY 2 Sheets-Sheet 2 Filed Nov. 3, 1958 lNVEA/TOR JACQUES OSM/ALD 8) 731552 ATTORNEY 2,948,866 C Fa tented Aug. 9, 1 ,9 0,

ADJUSTABLE coanncrmo NETWORKS Jacques Oswald, Versailles, France, assignor to Compagnie Industrielle des Telephones, Paris, France, a French corporation Filed Nov. '3, 1958, Ser. No. 771,566 4 Claims. Cl. 333-28 In copending application Serial Number 559,965; filed January 18, 1956, is disclosed a correcting network with adjustable attenuation and constant impedance",'cornprising a cut-all lattice type'network,'of which two opposite branches are formed of two resistances Ra, Rb, variable in such a Way that'their product remains constantly equal the square of the characteristic impedance R of the network, and of which the two other branches are formed by fixed impedances Z and Z', of which the product is equal to R for all the frequencies.

In said copending application the case has been specially in which the fixed impedances are reactances. In this case, the curve of the attenuation caused by the correcting network, as a function of the frequency of the Noltage applied thereto, comprises a certain number of pivot points, corresponding to privileged frequencies for which the attenuation does not depend on the adjustment of the resistances of the correcting network. q

There is, however, no frequency range inwhich the attenuation remains constant.

Now, it is nevertheless highly desirable to produc correcting networks of which the attenuation remains constant- (equal to a fixed reference value), for all the frequencies comprised outside a certain band, while for the frequencies comprised inside said band, the attenuation varies according to a given function of the frequency, dependent upon a parameter.

By placing such correcting networks in series, each ensuring a given variation of attenuation in the frequency band to which it belongs, it would then be possible to obtain a desired attenuation in the whole of the bands consituting the range in which the correction is to be fi c i.

- In the following an explanation will be given of how such a result can be obtained, in accordance with the present invention, reference being had to the drawings in which: 7

v Figure 1 illustrates a correcting network of the type described in the aforementioned co-pendingapplicationg' Figure 1' is a lattice-type network of the type useful O in Figure. 1; Fi gure;2 is a schematic illustration of a correcting network according to the present invention; x

Figures3 and 4 are filter networksutilized in connec-. tion with the circuit of Figure 2; and U Q Figure 5 is a curve of attenuation versus frequency for one example of thepresent invention.

First of all the structure and properties of the correcting network with constant impedance according to the above-mentioned patent application will be re called.v

In one of its embodiments, this correcting network, of characteristic impedance R, consists of a bridged-T (Fig.

1 2 with a resistance R on the output terminals of the. network Q.

The cut-all network, represented in Fig. l, is an antimetric lattice-type network of which two opposite branches are resistances Ra, Rb, adjustable in such a way that their, product remains equal to a fixed value R the two other opposite branches having respectively impedances R is the characteristic impedance of the network, linked to R and R by the relation -Ira vFor this correcting network, the resistance R and the transformation ratio a of thetransformer T (ratio oft he number of turns of the secondary winding to that of the primary winding) are respectively determined by:

which the effect is limited to a certain frequency domain; i.e. to one or more frequency zones for which it gives an attenuation variable in accordance with an imposed law, while outside this zone or zones, its attenuation is reduced to a fixed reference value. v 1

The correcting network according to the present invention, which makes it possible to achieve this result, is characterised in this, that the impedances of the two fixed branches of the cut-all network are respectively com-' posed of the input impedances of two inverted filters, .i.e. filters such that the impedance matrix of the one is equal," within the factor R to the admittance matrix of the other, the output terminals of said filters being closed on resistances equal to R the elements of these filters being determined in such a way that in order to obtain that" the adjustment of the-correcting network affects the at te'nuation caused by the latter only in a certain frequency l) of which the horizontal branches are each composed band, while in the external band or bands said attenua tion remains substantially constant and independent of this adjustment, said filters admit said band as attenuated band and the external band or bands as pass-bands,

Fig; 2 represents schematically a correcting network constituted in this way. It has been shown in the patent application cited above (Formulae 4 and 14) that the transfer exponent 0 of a correcting network according to said patent is given by the relation:

0a Z- R0 E (4) Tanh 2 -p-- R0 tanh V in which the factor p is equal to: V

and in which n designates the attenuation of the corecting network for p=0, i.e. for R =R ==R this atte nuation being, at all the frequencies equal to:

Now it is known that, for the frequencies. comprised in the' bands in which the composite attenuation of the filter is negligible, the effective input impedance of; the filter is substantially equal to the impedance. connected to its output terminals; the second factor" of the"riglit' band side of (4) is therefore very close to zero consequently 0 is substantially identical with a the eer recting network therefore only introduces a constant attenuation. In the attenuated bands, on the other hand, the effective impedance is variable, and consequently also the attenuation introduced by the correcting network. The mathematical relations will now be established which the elements of the correcting network according to the invention have to satisfy. For this purpose, the effective reflection exponent |"",.=A,-1- 'B of the filter F will be introduced, having an efiective input impedance Z bound to I, by the relation:

Fr F e 01' 7 z=R cot g while, in the above-mentioned patent, the impedance Z was defined by:

s 2:12 coth The transfer exponent of the correcting network will therefore be obtained by substituting and, by separating the real and imaginary parts, we find, designating by a the attenuation of the correcting network.

2116-14., 1-I-Me-2A, This Formula 12 makes it possible to specify the behaviour of the correcting network. In the pass-bands, the reflection attenuation A is very high, so that a remains practically equal to n It should be noted that the obtainment of a constant attenua- (12) tanh (er-a cos B tion equal to a fixed value independent of the -adjust ment of the corrector, outside the frequency band in which the correcting network can act, constitutes an indubitably exclusive advantage of the type of correcting network according to the invention: in the Bode correctors, in effect, attenuations are obtained in the pass 55 hand of the filters which certainly remain substantially constant, but which depend on the resistances connected to the terminals of these filters, i.e. on the adjustment of the correcting network.

In the attenuated bands, A, is negligible, the effecv tive impedance then being very close to a reactance, so that Z R Z R,

is substantially equal to 1; it follows that:

I =2. (12) tanh (a a cos B The curve of the attenuation produced by the corrector, as a function of the frequency of the voltage applied thereto, therefore has pivot points, independent of the adjustment of the correcting network, for the frequencies corresponding to 4 a (h being any whole number) for which the input impedance Z of the filters is equal to 'R and this curve shows maxima variations for all the adjustments of the corrector, at frequencies corresponding to: B =h1r for which the impedance Z shows a zero or a pole.

In the attenuated bands, for the frequencies sufficient- 1 1y far from the cut-off frequency, the input impedance Z of the filters differs little from their image impedance W regarded from their input terminals; the pivot points of the attenuation curve therefore substantially correspond to the frequencies for which the image impedance of the filters assumes the values ijR On the other hand, for the frequencies for which the variation of attenuation is maximum, the image impedance W of the filters shows the same singularity (zero or pole) as their eifective input impedance Z; these frequencies are therefore defined strictly by the poles or zeros of the image impedance.

In the vicinity of the cut-off frequencies of the filters, must be determined by the formula:

in which W designates the second image impedance of the filters, W their characteristic impedance (W ==W W and q their attenuation function.

According to whether it is desired to obtain an equalizer operating for frequencies lower than a given frequency, or higher than a given frequency, or comprised between two given frequencies, low-pass filters or band-cut filters will be chosen for the filters F and F.

The determination of the elements of the oorrector network is thus reduced to that of a filter of which the reflection exponent assumes given values for given frequencies; this is a well-known problem which can be solved by a method of approximation.

It is obvious that instead of the bridged-T arrangement, the equivalent differential arrangement described in the above-mentioned patent application can be used.

By way of example, a correcting device has been carried out for a wide frequency band, comprised between.

quencies of maximum attenuation) are regularly distributed in said scale, that of the first elementary corrector being equal to 300 kc./s., that of the pth being to and that of the sixteenth to 12,000 kc./s. The ratio of the middle frequencies of two adjacent elementary correctors is thus equal to 1.279; these frequencies are re 'spectively 802 kc./s., 1026 kc./s. and 13 12 kc./s. for

the 5th, 6th and 7th correctors. The filters F and F' forming the opposite branches of the cut-all network are band-cut filters, of inverse impedances, of which the diagrams are given in Figs. 3 and 4 respectively.

By replacing cos B, by 1 and ,u. by tanh (p-tanh g hence a a z a By choosing for a a value of 0.25 neper, the mean stasis r characteristicfimpedance R of the cut-all network is equal to- R/2, that is to, say to 37.5 ohms ifthe correcting network is adapted to impedances of 75 ohms.

, For the 'cb'r'rectoi S of which the middle frequency is f =lQQ6 kc./s., and which operates in a frequency band substantially limited by the middle frequencies of theadjacent correctors, the elements have been chosen thus:

a-a (Centif/fo fa/f Fig. 5 represents the attenuation curves of the 5th, 6th and 7th cor-rectors for =0.8; of course the adjustment of each corrector is independent, so that the ordinates of each curve of deviation can be multiplied separately by a positive or negative factor comprised between (--1) and (+1), if 0.8 be allowed as absolute maximum value of p, and between (-1.25) and (+1.25) if this value be raised to 1.

In the event that the correcting network according to the invention is used in a system of telecommunication by cable, comprising amplifiers and equalisers, it makes it possible to correct with great accuracy the deviations of attenuation due to systematic and uncertain imper fections of said amplifiers and equalisers.

The correcting networks according to the present invention can be carried out with great economy: in the example just described, each correcting network comprises in addition to the capacitors of which the cost is relatively low, four inductances and one transformer; which is substantially equivalent, from the point of view of cost, to five inductances. The total cost of the correeling device comprising sixteen elementary correcting networks is therefore of the order of the cost of eighty inductances, that is, substantially less than that of equivalent correctors of the well-known type.

What I claim is:

1. In a transmitting line an attenuation-correcting network comprising a main bridged-T four-terminal network including two horizontal branches each comprising a resistance equal to R, a vertical branch including the primary winding of a transformer, and a bridge branch including the input circuit of a cut-all antimetric auxiliary four-terminal network having a mean characteristic impedance R the output circuit of said auxiliary four-terminal network being connected to the secondary winding of said transformer, said auxiliary four-terminal network being a lattice-type network and comprising a first pair of opposite branches comprising resistances adapted to be varied while maintaining their product equal to RF, and a second pair of opposite branches including fixed impedances of which the product is also equal Stet-R52, wherein" said fixed impedances include respectively theinput circuit of two filters of which the outputcircuits are each connected, respectively, to a resistance R0,, said filters being adapted to have a nonzero composite' attenuation throughout the domain of correction and a negligible composite attenuation outside said domain, 1 whereby said attenuation-correcting network only alfects theelfective attenuation in a definite frequency band.

, 2. In a transmitting line an attenuation correcting" branches including a resistance equal to the value of the" constant characteristic impedance of the line, and at least one cut-all antimetric auxiliary four-terminal network, the input thereof being inserted in said bridge branch and the output thereof being coupled with said vertical branch, said auxiliary four-terminal network being a lattice-type network and having a mean characteristic impedance R and comprising a first pair of op posite branches having resistances which are adapted to vary while maintaining their product equal to R and a second pair of opposite branches including fixed impedances of which the product is also equal to R wherein said fixed impedances include the input circuits of two filters of which the output circuits are connected each to a respective resistance of R, value, said filters being adapted to have a non-Zero composite attenuation in a certain frequency band, and a. negligible composite attenuation outside said frequency band whereby said attenuation correcting network only aflects the produced attenuation throughout a domain of correction including said frequency band.

3. In a transmitting line a plurality of attenuation,- correcting networks inserted therein, said attenuationcorrecting networks being series connected in said transmitting line, wherein each of said attenuation-correcting networks comprises a main bridged-T four-terminal network including two horizontal branches one vertical branch andone bridge branch, each of said horizontal branches including a resistance equal to the value of the line constant characteristic impedance, cut-all antimetric auxiliary four-terminal networks being associated respectively with each of said main bridged-T four-terminal networks, each auxiliary network being a lattice-type network and having input and output circuits; wherein the input circuit of each auxiliary four-terminal network is inserted in the bridge branch of the associated main four-terminal network, the output circuit of the same being coupled with the corresponding vertical branch; wherein each of said auxiliary four-terminal networks has a corresponding mean characteristic impedance and comprises a first pair of opposite branches having resistances which are adapted to vary while maintaining their product equal to the square value of said corresponding mean characteristic impedance and a second pair of opposite branches including fixed impedances of which the product is also equal to the square value of said corresponding mean characteristic impedance; wherein said fixed impedances include the input circuits of two filters, the output circuits of said filters being connected each to a respective resistance of value equal to said corresponding mean characteristic impedance and said filters in each of said attenuation-correcting networks being adapted to have a non-zero composite attenuation within corresponding given frequency band and a negligible composite attenuation outside said corresponding frequency band whereby each of said attenuation-correcting networks can be adjusted independently so as to define a zone of correction for said plurality of attenuation-correcting networks which includes the various corresponding frequency bands.

4. In a transmitting line an attenuation-correcting network comprising a main T network including two horizontal branches and a vertical branch, at least one cutall antimetric auxiliary four-terminal network having a mean characteristic impedance R the input circuit of said auxiliary four-terminal network being coupled with each of said horizontal branches, and the output circuit of said auxiliary four-terminal network including said vertical branch, said vertical branch having a resistance value which is in relation with the line constant characteristic impedance, said auxiliary four-terminal network being a lattice/type network comprising a first pair of opposite branches including resistances which can be made to vary while maintaining their product equal to R and a second pair of opposite branches including fixed impedances of which the product is also equal to R said filters being'adapted to have a non-zero com-' posite attenuation throughout the domain of correction.

and a negligible composite attenuation outside said domain, whereby said attenuation-correcting network only affects the effective attenuation in a definite frequency band.

References Cited in the file of this patent FOREIGN PATENTS 1,116,277 France Ian. 30, 1956 

